Hillary Clinton won primaries in Florida, North Carolina and Ohio, the night's most contested prize, as her rival, Sen. Bernie Sanders, struggled to get the boost he needed to try to close the gap in the race for the Democratic presidential nomination.

Clinton also won a close contest in Illinois and was holding an extremely small margin in Missouri, with nearly all of the votes counted. With those contests so close, neither candidate will gain a significant edge from them in the race for delegates to the Democratic nominating convention this summer. Clinton's three big victories, by contrast, will give her a major gain.

“We are moving closer to securing the Democratic Party nomination and winning this election in November,” Clinton told supporters here, and she quickly moved to an attack on the Republican she expects to face in that election, Donald Trump, whom she accused of offering “bluster and bigotry.”

“Our next commander in chief has to be able to defend our country, not embarrass it; engage our allies, not alienate them,” she said.

“When we hear a candidate for president call for rounding up 12 million immigrants, barring all Muslims from entering the United States, when he embraces torture, that doesn't make him strong — it makes him wrong.”

Clinton barely mentioned Sanders, the independent senator from Vermont, except to briefly congratulate him for running a “vigorous campaign.”

If Sanders was chastened by the results, he didn't let it show while speaking to rapturous supporters in Phoenix.

“Do not settle for the status quo when the status quo is broken,” he said in a speech in which he showed no sign of easing up on Clinton. He once again attacked her vote in favor of the war in Iraq and demanded she release the transcripts of lucrative speeches to Wall Street firms.

Sanders had worked aggressively over the last week to expand a beachhead in the nation's industrial states after his upset victory in Michigan last week exposed new vulnerabilities for Clinton.

That set up Ohio as a key contest, where both candidates campaigned extensively and spent large amounts on television advertising. Clinton's victory there will go a long way toward solidifying her margin in the delegate race and reassuring her supporters.

Clinton's victory in North Carolina continued her sweep through the South, where black voters make up a big share of the Democratic electorate. And her decisive win in Florida, where she took nearly two-thirds of the vote, will net her a large majority of the state's 246 delegates to the Democratic convention — the third-largest delegation after California and New York.

The wins mean Clinton will significantly expand her already large lead among delegates to this summer's convention, building a margin of roughly 300 delegates over Sanders, without counting the roughly 400 so-called superdelegates who back her — party leaders and elected officials who automatically get convention votes.

After Tuesday, the math looks increasingly daunting for her rival, who now would need a series of very big victories in big states to catch up with Clinton's growing lead in the delegate race.

That does not, however, mean she has clinched the nomination. Under the Democrats' rules, which allocate delegates proportionately to each candidate's vote, Clinton probably won't be able to do that until the primary season ends in California in June.

In the Michigan upset last week, frustration among Midwestern Democrats with some of the free-trade policies Clinton has backed over the years, as well as with the Wall Street institutions whose recklessness helped push the nation into recession in 2007, emerged as a significant liability for the former secretary of State.

That anger shaped the campaigns in the three Midwestern states. Polls had indicated that all three could have close contests, and after the big miss by pollsters in Michigan, all of whom predicted a Clinton victory, both campaigns were wary of predictions.

Sanders' attacks on corporate America, particularly on trade, clearly connected with many voters.

“I believe in his change,” said Sanders supporter Mark Russell, 59, who stopped to vote in the Clintonville neighborhood of Columbus, near Ohio State University, on his way to work at Goodwill Industries.

“I believe that right now we're run by corporations,” he said. “It's not an even playing field, and it counts against us. I believe that he can do something about that. He's the only one that's really talking in that direction.”

Yet Sanders' effort to translate that sort of sentiment into votes came up short this time.

Clinton continues to do well with voters like Tampa resident Zachary Hines, 26, who value her years of preparation.

“She's the most prepared and experienced candidate to run for president in modern history,” said Hines, who works as a marketing director for a theater company. “I'm very excited to vote for the first woman president.”

Exit polls suggested voters were more confident in Clinton's agenda, with 77% in Ohio saying her policies were realistic, as opposed to 58% saying the same about Sanders' proposals. The divide was even bigger in Florida, where only 46% of voters expressed confidence that the Sanders agenda was realistic, according to exit polling conducted for the major television networks and the Associated Press.

Female voters came out in force for Clinton on Tuesday. She won 67% of them in Florida and 58% of them in Ohio, according to the exit poll. She also dominated with nonwhite voters in both states, winning 73% of them in Florida and 63% in Ohio. Seniors supported her by a margin of nearly 4 to 1 in both states.

Clinton had been eager to avenge a Michigan loss that some operatives attributed to poor strategic decisions and resource deployment by a campaign that had grown complacent after public polls that proved wildly misleading.

To ensure she did not repeat that defeat, Clinton redoubled her focus on the Midwest.

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The former secretary of State, who has locked up almost every major national union endorsement, mobilized her labor supporters and stepped up her opposition to the Trans Pacific Partnership, the trade deal negotiated by President Obama that is reviled by unions.

She boasted of having voted for the bailout bill that in part saved U.S. car companies from collapse, and vigorously defended herself against Sanders' attacks.

“We have like less than 5% of the world's population,” she said Monday at a town hall hosted by MSNBC in Springfield, Ill. “We have to trade with the other 95%. His position is so ‘anti.' He is against things before they are even finished, before they are read,” she added. “He just is reflexively against anything that has any international implication.”

Earlier that day, Clinton expressed outrage that a heavily subsidized Nabisco factory in the Chicago area was in the process of laying off workers and moving jobs out of state. She scolded Nabisco for not working harder to keep the plant intact, and she said firms like Nabisco that get tax breaks and then leave anyway “should have to pay that money back.”

The funds should “be used to reinvest in the community and the workers,” she said.

In the process of winning over Democrats in the Rust Belt, Clinton began to sound a lot like her more progressive rival — so much so that activists who often agree with him declared victory Tuesday night.

“Hillary Clinton won Ohio and had a Super Tuesday by riding the economic populist tide instead of fighting it,” said a statement from Adam Green, co-founder of the Progressive Change Campaign Committee. “That was almost unimaginable a year ago.”

“The primary continues — but no matter who wins, the center of gravity has fundamentally shifted in the Democratic Party,” Green wrote.

But Sanders is not going away. His impressive fundraising machine continues to churn, and there is every indication it will do so until every state has voted. Even as winning the nomination becomes increasingly unlikely, the Vermonter will be there to push Clinton leftward.

Sanders put considerable energy over the last week into criticizing Clinton over her centrist record, warning voters that she only recently had adopted some of the progressive economic positions he has embraced his entire career. Clinton can expect a continuation of Sanders' attacks on the millions of dollars in speaking fees and campaign contributions that she and the super PAC supporting her have accepted from Wall Street firms.

“She's now on my side on many issues,” Sanders said Monday night at a separate MSNBC town hall at Ohio State. “But the question is, where were you when it mattered?”

Halper reported from Washington and Mason from West Palm Beach. Times staff writer Mark Z. Barabak contributed to this report from Columbus, Ohio.